Subjective Probability

Subjective probability is the opinion or probable outcome based on an individual’s perspective, personal experience, and sense of judgment. It is entirely based on an individual’s belief system so it differs from person to person, and there is no set pattern to derive it. It aims to quantify the degree of belief or confidence an individual has in the occurrence of an event.

The subjective probability theory is not based on the quantitative determination. Instead, it only reflects the views of a person regarding the occurrence or otherwise of any particular event process or desired outcome. For example, an investor following their gut feeling in trading is a common example of subjective probability.

• Subjective probability refers to the probability of an event occurring or otherwise based on an individual’s experience and personal judgment. This may depend completely on their beliefs and views.
• There is no mathematical formula or calculations to deriving this probability as it comes from how a person views a situation.
• Classical, objective, and empirical probabilities are different kinds of probabilities that differ from subjective probabilities. 
• It is not mandatory that the probability based on an individual’s belief would always be accurate as it is heavily influenced by personal bias.

Subjective probability refers to judging a particular outcome, specific events’ occurrence, or otherwise based on personal experience, knowledge, and gut feeling. Such probability is not backed by historical data or concrete evidence. In all possibilities, it is just a desired outcome that a person has made out of their perspective, nature, belief, and common sense.

Subjective probability differs for everyone; there can be multiple probabilities for a single scenario, as each person can have their own experience. People without experience can also judge something based on personal beliefs and assumptions.

Many analysts and researchers like to define subjective probability as guesswork and hunches made by people with minimum knowledge and understanding of situations. Though it is applied in many different ways and has a wide scope, it can backfire as records, patterns, or strong analyses do not back it. For critical scenarios, replacing any other type of probability is better. One of its key limitations is that everyone can bring their own experience to determine the desired outcome. A higher degree of personal bias, perception, and individual opinion influences the likelihood of an event occurring or otherwise.

Check out these examples to get a better idea:

Example #1

John is an ace investor and has been investing and studying the stock market for nearly nine years. He has filtered many publicly listed companies he is confident will perform well and give enormous returns.

He is well-reputed in the trader’s community, and many people often come to John for investment suggestions. John’s prior investments have already reaped him exponential returns, and based on his judgment, he is confident that the new investment will also pay off well. Here, John makes trading decisions based on his gut instinct and past experiences.

Now, it is reasonably possible that John’s investments can backfire since they are not based on any fundamental study, indicators, or stock market ratios. But it is also understandable that people tend to believe his predictions because they are proven to be right before.

Example #2

Another good subjective probability example in real life can be described with the case of John’s brother Jamie. Every day, Jamie has boarded a particular local train for the past nine months to reach his office in the main city. Over the past years, he has observed that the train has been late every Tuesday by eighteen minutes. Jamie explained the same when a coworker asked him to help with train routes.

Again, it is a matter of probability, and it may happen that one day Jamie and his coworker will take the schedule lightly, thinking the train will again be late, and it may not. This will result in Jamie and his colleague missing the train and being late for work.

The followings are the pros and cons of subjective probability:

Advantages

• Since it is based on prior experience and personal judgment, the prediction is easier.
• It helps forecast future business performance, which eventually helps in firm decision-making.
• Businesses can predict sales, profit, and individuals can predict the occurrence of an event or the most likely result.
• The subjective probability may be used in planning individual tasks and daily life routines based on multiple subjective probabilities.

Disadvantages

• There is no concrete calculation. Therefore, any result is eventually an abstract probability.
• It is backed by gut feelings, personal views, and individual experiences, which readily differ from one person to another.
• There are multiple individual opinions, so choosing anyone is hard.
• Even the subjective probability must adhere to some factors and conditions and must be taken seriously.

• Classical probability refers to outcomes based on practical reasoning. Empirical probability is based on historical data, and objective probability is based on the analysis of chances. In contrast, subjective probability is based on gut instinct and personal belief.
• Out of all types of probability, only subjective probability assessment depends on experience and personal judgment. In comparison, all the others are based on some form of calculation.
• A 50% chance of getting a head is the classical probability when tossing a coin. If the record suggests more chances of a head coming, it is an empirical probability. If certain measures based on concrete analysis were taken during the toss to understand the probability of a head side, it is objective probability. In comparison, without any data or evidence, just an instinct or judgment that the result of a coin toss will be heads is subjective probability.
• Subjective probability has no formula, whereas all the other probabilities have a calculated probability equation.

This article has been a guide to what is Subjective Probability. We explain its examples and compare it with classical, empirical, and objective probability. You may also find some useful articles here -

• Posterior Probability
• Conditional Probability
• A Priori Probability